When the dose-finding phase is completed, treatment will begin. Patients will take riluzole or placebo (a look-a-like pill with no active ingredient) twice a day, along with their regular Sinemet, for 3 weeks. (All participants will receive placebo at some time during the study, and some patients will receive only placebo throughout the entire 4 weeks.) At the end of each week, patients will be readmitted to the hospital and receive the previous week's dose of riluzole or placebo in combination with a levodopa infusion at the rate determined in the dose-finding phase of the study. The procedure for the infusion will be the same as that for the dose-finding phase. The dose of riluzole will be increased until the optimum dose has been achieved or until side effects occur (at which time the dose will be lowered or the drug stopped).